--

The International Mathematical Knowledge Trust (IMKT) aims to represent digital mathematical knowledge in a deeply semantic way. Building on recent discussions and strategic advancements at the ICM 2026 and ICMS 2026 conferences, this talk will report on the latest global milestones. Furthermore, we will discuss how Germany's research data infrastructures (specifically zbMATH Open and MaRDI) can actively support and shape this international movement, fostering a globally connected ecosystem for mathematical knowledge.

Computational Science and Engineering relies on complex, multi-step workflows that combine simulations, data processing, and parameter-driven analyses across heterogeneous environments. Ensuring reproducibility in such settings requires not only abstract workflow descriptions but also semantically rich metadata that is interoperable across domains.

In this work, we present MaRDIflow, a lightweight, metadata-driven workflow framework developed within the MaRDI consortium for research data management in the mathematical sciences. MaRDIflow executes workflows through explicit input–output relationships between components, enabling structured metadata descriptions at different abstraction levels. Redundant representations of models, code, and data are supported to strengthen reproducibility and reuse.

To address semantic interoperability, MaRDIflow integrates domain specific ontologies via RESTful APIs and SPARQL endpoints. A modular ontology layer, built on an extensible abstract base class, allows for integration of domain-specific ontologies with minimal effort. With that, workflow components and their metadata to can be aligned dynamically with standardized vocabularies during both construction and execution. As a concrete example, we integrate Voc4Cat, a domain-specific SKOS vocabulary from the NFDI4Cat consortium. Through this integration, knowledge graphs are used to represent and query relationships across workflow layers, supporting automated discovery, validation, and consistent interpretation of data.

The presented use cases demonstrate how combining workflow descriptions with domain ontologies enhance semantic consistency, interoperability, and reproducibility. This work further highlights the practical role of application ontologies and lays the groundwork for extending MaRDIflow with additional NFDI ontologies across disciplines.

Mathematical models are among the central research objects of mathematics and its applications. However, they are usually documented only indirectly: in publications, software repositories, datasets, or project-specific descriptions. Essential information – assumptions, defining equations, model variants, corresponding research problems, associated computational tasks, and implementations – is scattered across different sources and communities. This makes it often difficult to find existing models, compare related formulations, and reuse mathematical knowledge beyond the original publication context.

Within the Mathematical Research Data Initiative (MaRDI), the mathematics consortium of the German National Research Data Infrastructure (NFDI), the Mathematical Models Database (MathModDB) addresses this problem by treating mathematical models explicitly as structured research data. MathModDB represents models and their surrounding mathematical context in a knowledge graph, linking academic disciplines, research problems, formulations, quantities, computational tasks, and publications. Users can navigate from a research problem to suitable model classes, inspect and compare different formulations of a model, and identify related models across disciplines.

In this talk, we present the status of MathModDB and its integration into the MaRDI ecosystem. We describe the underlying ontology, the representation of mathematical knowledge in the graph, and the workflow for adding and reviewing model information. Since MathModDB is integrated in the MaRDI Portal, which builds on Wikibase technology, the community can contribute directly: models can be entered through guided questionnaires in MaRDMO – a MaRDI extension of the research data management planning tool RDMO – or edited via the portal's web interface, and contributions can be manually reviewed to maintain consistency with the underlying ontology.

We illustrate the approach with examples from applied mathematics, showing how models are connected to research problems, defining formulations, and related resources. We also touch upon ongoing work on linking MathModDB to executable model representations such as ModelingToolkit.jl, and on the long-term maintenance of mathematical knowledge beyond the current funding period, where relying on open standards and Wikibase technology keeps a migration path towards community-driven infrastructures open. A key challenge, finally, is community-driven curation: a knowledge graph of mathematical models can only thrive through contributions and review from the mathematical community itself – an effort for which MaRDI builds on its partnership with professional societies such as the DMV.